Studies of the Sign Problem:

The sign problem hinders progress in understanding many strongly coupled
quantum systems. Mattias Troyer and I have shown that
some sign problems are NP-hard, and thus practically impossible to solve.
This means that no generally applicable method to solve all sign problems can
exist. Still, the meron-cluster algorithm, and
the more recently developed nested cluster
algorithm can be used to either completely solve or at least substantially
alleviate very severe sign problems.